Linear Parameter-Varying (LPV) systems can be used as a bridge to extend the well studied model based control methods of Linear Time-Invariant systems to certain nonlinear systems. Despite significant attention in literature over the last two decades, finding an efficient global state space identification algorithm remains an open problem. Furthermore, a common assumption has been that the scheduling signals governing the time-varying dynamics are known or measured exactly. These drawbacks are found to inhibit the number of use cases for model based LPV control. This thesis explores new ways of identifying LPV systems for more general nonlinear systems with limited information on the optimal scheduling variable and scheduling dimension.

To this end, two novel rank constrained least squares problems are presented to identify system matrices and scheduling signals from input and full state measurements, and a dictionary of possible scheduling signals. The use of the methods is demonstrated in a simulation experiment, and the results are compared to existing full state measurement methods.

At last, the full state measurement methods are coupled with a state sequence estimation method from literature in order to obtain a method for identification of quasi-LPV systems from Input-Output measurements. Here "quasi" indicates that the scheduling signal is dependent on the system state and input. The scheme is flexible, and a proof of concept is given on a small nonlinear system.